Approximating the Minimum Equivalent Digraph

Approximating the Minimum Equivalent Digraph

1 Introduction

Approximating The Minimum Equivalent Digraph

Approximating the Minimum Tour Cover of a Digraph

Given a directed graph G with non-negative cost on the arcs, a directed tour cover T ofG is a cycle (not necessarily simple) inG such that either head or tail (or both of them) of every arc in G is touched by T . The minimum directed tour cover problem (DToCP), which is to find a directed tour cover of minimum cost, is NP -hard. It is thus interesting to design approximation algorithms with per...

Approximating the Minimum Bisection Size

A bisection of a graph with n vertices is a partition of its vertices into two sets, each of size n=2. The bisection size is the number of edges connecting the two sets. Finding the bisection of minimum size is NP-hard. We present an algorithm that nds a bisection that is within O(p n log n) of optimal. No sublinear approximation ratio for bisection was previously known.

Approximating the minimum cycle mean

We consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight. Our contributions are twofold: (1) First we show that the algorithmic question is reducible in O(n2) time to the problem of a logarithmic number of min-plus matrix multiplications of n× n-matrices, where n is the...